Solve the System of Equations -x-4y=2 and x+4y=-2

$- x - 4 y = 2$ and $x + 4 y = - 2$

Subtract $4 y$ from both sides of the equation.

$x = - 2 - 4 y$

$- x - 4 y = 2$

Replace all occurrences of $x$ with $- 2 - 4 y$ in each equation.

Replace all occurrences of $x$ in $- x - 4 y = 2$ with $- 2 - 4 y$ .

$- (- 2 - 4 y) - 4 y = 2$

$x = - 2 - 4 y$

Simplify the left side.

Simplify $- (- 2 - 4 y) - 4 y$ .

Simplify each term.

Apply the distributive property.

$2 - (- 4 y) - 4 y = 2$

$x = - 2 - 4 y$

Multiply $- 1$ by $- 2$ .

$2 - (- 4 y) - 4 y = 2$

$x = - 2 - 4 y$

Multiply $- 4$ by $- 1$ .

$2 + 4 y - 4 y = 2$

$x = - 2 - 4 y$

$2 + 4 y - 4 y = 2$

$x = - 2 - 4 y$

Combine the opposite terms in $2 + 4 y - 4 y$ .

Subtract $4 y$ from $4 y$ .

$2 + 0 = 2$

$x = - 2 - 4 y$

Add $2$ and $0$ .

$2 = 2$

$x = - 2 - 4 y$

$2 = 2$

$x = - 2 - 4 y$

$2 = 2$

$x = - 2 - 4 y$

$2 = 2$

$x = - 2 - 4 y$

$2 = 2$

$x = - 2 - 4 y$

Remove any equations from the system that are always true.

$x = - 2 - 4 y$

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